In economics, the elasticity y,x measures the percent change in a variable y after a 1% change in a variable x. Mathematically, such elasticty is: y,x = y/x x/y , if |y,x| > 1 the effect is said to be elastic, whereas if 0 |y,x| < 1 the effect is inelastic.

a) Show that the parameters in the following regression y = x 1 1 x 2 2 can be interpreted as elasticities. How would you estimate 1 and 2 using a linear regression?

b) A single producer with full market power has a cost of production T C(q) and faces a downward sloping demand p(q). Use profit maximization principles to show that optimal production is such that: p M(q ) 1 + 1 q,P = MC(q ), where MC(q) is the marginal cost, q is the optimal production level, q,P is the price elasticty of demand, and p M(q) is the price set by the monopoly. (Hint: use the first order condition of the profit maximization problem)

c) If p(q) = 140 2q, and T C(q) = 1000 + 0.5q 2 , what is the price elasticity of demand and what is the price set by the monopolist?