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On the Direction of Innovation Hugo A. Hopenhayn Francesco Squintani EARIE, Milan August 2014 Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation Introduction Most research on patents asks: Is IP sufficient or

On the Direction of Innovation Hugo A. Hopenhayn Francesco Squintani EARIE, Milan August 2014 Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation
Introduction Most research on patents asks: “Is IP sufficient or excessive?” This paper: “Does it go in the right direction?” Basic theory: heterogenous patent races: hotter and cooler Equilibrium allocates scarce researchers to different patent races. Equilibrium and optimal allocation will rarely coincide. Under plausible assumptions, too many researchers in hot areas Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation
Introduction Most research on patents asks: “Is IP sufficient or excessive?” This paper: “Does it go in the right direction?” Basic theory: heterogenous patent races: hotter and cooler Equilibrium allocates scarce researchers to different patent races. Equilibrium and optimal allocation will rarely coincide. Under plausible assumptions, too many researchers in hot areas Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation
Introduction Most research on patents asks: “Is IP sufficient or excessive?” This paper: “Does it go in the right direction?” Basic theory: heterogenous patent races: hotter and cooler Equilibrium allocates scarce researchers to different patent races. Equilibrium and optimal allocation will rarely coincide. Under plausible assumptions, too many researchers in hot areas Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation
Introduction Most research on patents asks: “Is IP sufficient or excessive?” This paper: “Does it go in the right direction?” Basic theory: heterogenous patent races: hotter and cooler Equilibrium allocates scarce researchers to different patent races. Equilibrium and optimal allocation will rarely coincide. Under plausible assumptions, too many researchers in hot areas Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation
Introduction Most research on patents asks: “Is IP sufficient or excessive?” This paper: “Does it go in the right direction?” Basic theory: heterogenous patent races: hotter and cooler Equilibrium allocates scarce researchers to different patent races. Equilibrium and optimal allocation will rarely coincide. Under plausible assumptions, too many researchers in hot areas Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation
Introduction Most research on patents asks: “Is IP sufficient or excessive?” This paper: “Does it go in the right direction?” Basic theory: heterogenous patent races: hotter and cooler Equilibrium allocates scarce researchers to different patent races. Equilibrium and optimal allocation will rarely coincide. Under plausible assumptions, too many researchers in hot areas Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation
A simple model Two research areas (patent races), one potential discovery each. Social and private value of discovery z 1 < z 2 . Total M homogenous researchers. Discovery with probability p ( m j ). Compare competitive and optimal allocations Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation
A simple model Two research areas (patent races), one potential discovery each. Social and private value of discovery z 1 < z 2 . Total M homogenous researchers. Discovery with probability p ( m j ). Compare competitive and optimal allocations Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation
Competitive equilibrium and optima Expected probability of discovery for a researcher in area j : p ( m j ) / m j Equilibrium m 1 + m 2 = M and p ( m 1 ) p ( m 2 ) z 1 = z 2 m 1 m 2 Social planner maximizes z 1 p ( ˜ m 1 ) + z 2 p ( ˜ m 2 ) so: z 1 p ′ ( ˜ m 1 ) = z 2 p ′ ( ˜ m 2 ) In both cases m 2 > m 1 Wedge p ( m ) / m p ′ ( m ) > 1 for concave p ( m ) Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation
Competitive equilibrium and optima Expected probability of discovery for a researcher in area j : p ( m j ) / m j Equilibrium m 1 + m 2 = M and p ( m 1 ) p ( m 2 ) z 1 = z 2 m 1 m 2 Social planner maximizes z 1 p ( ˜ m 1 ) + z 2 p ( ˜ m 2 ) so: z 1 p ′ ( ˜ m 1 ) = z 2 p ′ ( ˜ m 2 ) In both cases m 2 > m 1 Wedge p ( m ) / m p ′ ( m ) > 1 for concave p ( m ) Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation
Competitive equilibrium and optima Expected probability of discovery for a researcher in area j : p ( m j ) / m j Equilibrium m 1 + m 2 = M and p ( m 1 ) p ( m 2 ) z 1 = z 2 m 1 m 2 Social planner maximizes z 1 p ( ˜ m 1 ) + z 2 p ( ˜ m 2 ) so: z 1 p ′ ( ˜ m 1 ) = z 2 p ′ ( ˜ m 2 ) In both cases m 2 > m 1 Wedge p ( m ) / m p ′ ( m ) > 1 for concave p ( m ) Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation
Competitive equilibrium and optima Expected probability of discovery for a researcher in area j : p ( m j ) / m j Equilibrium m 1 + m 2 = M and p ( m 1 ) p ( m 2 ) z 1 = z 2 m 1 m 2 Social planner maximizes z 1 p ( ˜ m 1 ) + z 2 p ( ˜ m 2 ) so: z 1 p ′ ( ˜ m 1 ) = z 2 p ′ ( ˜ m 2 ) In both cases m 2 > m 1 Wedge p ( m ) / m p ′ ( m ) > 1 for concave p ( m ) Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation
Competitive equilibrium and optima Expected probability of discovery for a researcher in area j : p ( m j ) / m j Equilibrium m 1 + m 2 = M and p ( m 1 ) p ( m 2 ) z 1 = z 2 m 1 m 2 Social planner maximizes z 1 p ( ˜ m 1 ) + z 2 p ( ˜ m 2 ) so: z 1 p ′ ( ˜ m 1 ) = z 2 p ′ ( ˜ m 2 ) In both cases m 2 > m 1 Wedge p ( m ) / m p ′ ( m ) > 1 for concave p ( m ) Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation
Comparison From equilibrium conditions: p ( m 1 ) / m 1 = p ( m 2 ) / m 2 p ′ ( ˜ p ′ ( ˜ m 1 ) m 2 ) Proposition m 2 if ( p ( m ) / m ) Assume concave p ( m ) . Then m 2 > ˜ increases with p ′ ( m ) m . Proof. By contradiction. If m 2 ≤ ˜ m 2 then p ( m 2 ) / m 2 ≥ p ( m 2 ) / m 2 > p ( m 1 ) / m 1 ≥ p ( m 1 ) / m 1 p ′ ( ˜ p ′ ( m 2 ) p ′ ( m 1 ) p ′ ( ˜ m 2 ) m 1 ) contradicting the equality above. Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation
Comparison From equilibrium conditions: p ( m 1 ) / m 1 = p ( m 2 ) / m 2 p ′ ( ˜ p ′ ( ˜ m 1 ) m 2 ) Proposition m 2 if ( p ( m ) / m ) Assume concave p ( m ) . Then m 2 > ˜ increases with p ′ ( m ) m . Proof. By contradiction. If m 2 ≤ ˜ m 2 then p ( m 2 ) / m 2 ≥ p ( m 2 ) / m 2 > p ( m 1 ) / m 1 ≥ p ( m 1 ) / m 1 p ′ ( ˜ p ′ ( m 2 ) p ′ ( m 1 ) p ′ ( ˜ m 2 ) m 1 ) contradicting the equality above. Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation
Comparison From equilibrium conditions: p ( m 1 ) / m 1 = p ( m 2 ) / m 2 p ′ ( ˜ p ′ ( ˜ m 1 ) m 2 ) Proposition m 2 if ( p ( m ) / m ) Assume concave p ( m ) . Then m 2 > ˜ increases with p ′ ( m ) m . Proof. By contradiction. If m 2 ≤ ˜ m 2 then p ( m 2 ) / m 2 ≥ p ( m 2 ) / m 2 > p ( m 1 ) / m 1 ≥ p ( m 1 ) / m 1 p ′ ( ˜ p ′ ( m 2 ) p ′ ( m 1 ) p ′ ( ˜ m 2 ) m 1 ) contradicting the equality above. Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation
Generalization Set of innovations/goods indexed by z with distribution F ´ 1 Welfare/utility: 0 zp ( m ( z )) dF ( z ) ´ 1 Resource constraint: 0 m ( z ) dF ( z ) = M Equilibrium and optimal conditions same as before. p ( m ( z )) / m ( z ) = k (constant) p ′ ( ˜ m ( z )) Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation
Generalization Set of innovations/goods indexed by z with distribution F ´ 1 Welfare/utility: 0 zp ( m ( z )) dF ( z ) ´ 1 Resource constraint: 0 m ( z ) dF ( z ) = M Equilibrium and optimal conditions same as before. p ( m ( z )) / m ( z ) = k (constant) p ′ ( ˜ m ( z )) Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation
Bias Definition The competitive equilibrium is biased to hot areas iff there exists a z ∗ and m ( z ) < ˜ m ( z ) for z < z ∗ and m ( z ) > ˜ m ( z ) for z > z ∗ . If the opposite inequalities hold, we say it is biased to cold areas. Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation
Biased to hot areas m(z) m ~ m(z) * z Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation
Comparison p ( m ( z )) / m ( z ) = k (constant) p ′ ( ˜ m ( z )) Proposition The competitive equilibrium is biased to hot (cold) areas if the wedge p ( m ) / m is increasing (decreasing) in m . p ′ ( m ) Proof. Both in the equilibrium and optimum m (resp ˜ m ) are strictly m ( z ) . For any z ′ > z it follows increasing. Take z where m ( z ) = ˜ that p ( m ( z ′ )) / m ( z ′ ) > p ( m ( z )) / m ( z ) = k . p ′ ( m ( z ′ )) p ′ ( m ( z )) m ( z ′ ) < m ( z ) . So ˜ Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation
Comparison p ( m ( z )) / m ( z ) = k (constant) p ′ ( ˜ m ( z )) Proposition The competitive equilibrium is biased to hot (cold) areas if the wedge p ( m ) / m is increasing (decreasing) in m . p ′ ( m ) Proof. Both in the equilibrium and optimum m (resp ˜ m ) are strictly m ( z ) . For any z ′ > z it follows increasing. Take z where m ( z ) = ˜ that p ( m ( z ′ )) / m ( z ′ ) > p ( m ( z )) / m ( z ) = k . p ′ ( m ( z ′ )) p ′ ( m ( z )) m ( z ′ ) < m ( z ) . So ˜ Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

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