Assume that there are two consumers and two commodities. Let the utility functions be U1 = q11q12 and U2 = q21q22 with q11 + q21 =q1 and q12 + q22 = q2. Show that Scitovsky contours are given by q1q2 = (√U1 +√U2 )^2.
Prove that if the consumer is indifferent between commodity bundles (q⁰1........q⁰n) and (q¹1......q¹n) and has a homothetic utility function, she will also be indifferent between the bundles (t1q⁰1....tq⁰1) and (tq¹1....tq¹n)Q40
An entrepreneur uses two distinct production processes to produced two distinct goods, Q1 and Q2. The production function for each good is CES, and the entrepreneur obeys the equilibrium condition for each. Assume that Q1 has a higher elasticity of substitution and a lower value for the parameter α than Q2. Determine the input price ratio at which the input use ratio would be the same for both goods. Which good would have the higher input ratio if the input price ratio were lower? Which would have the higher use ratio if the price ratio were higher?

 

- Consider the following markets which are characterized by lagged supply response: (a) D, = 40 10p, ; S, = 2 + 9p.1- (b) D. = 30 5p: ; S = 20 pe1. Determine equilibrium price and quantity for each market. Assume an initial price 20 percent below the equilibrium price for each market, and determine the number of periods necessary for each price to adjust to within 1 percent of equilibrium