Assignment
1. (Returns to scale and economies of scale, 2nd round) Assume that the good q is produced using two inputs: capital and labour (K and L). Demonstrate that decreasing returns to scale need not imply diseconomies of scale.
2. (Partial and general equilibrium analyses) Bread and butter are complements in consumption (and unrelated in production).
(a) Illustrate and explain the partial equilibrium effect of technological improvement in butter production which lowers the marginal cost of producing butter (that is, the butter's supply schedule shifts to the right). [Note: You only need one diagram to support your explanation]
(b) Illustrate and explain the general equilibrium effect of technological improvement in butter production. [Note: You need two diagrams to support your explanation]
(c) Which one of your analyses leads to a higher price of butter?
3. (Pareto efficiency) A pizza is to be divided between Yoshi and Taka (both like pizzas). True or false? Pareto efficiency requires that they receive equal portions.
4. (General equilibrium 1) Jane has 3 litres of soft drinks and 9 sandwiches. Bob has 8 litres of soft drinks and 4 sandwiches. With these endowments, Jane's marginal rate of substitution (MRS) of soft drinks for sandwiches is 4 and Bob's MRS is equal to 2. Draw an Edgeworth box diagram to show whether this allocation of resources is efficient. If it is, explain why. If not, what exchanges will make both parties better off?
5. (General equilibrium 2) James and Karen treat left and right shoes as perfect (one-to-one) complements. James has 1 left shoe and 5 right shoes. Karen has 5 left shoes and 3 right shoes.
(a) Draw an Edgeworth box diagram that represents the above situation. Take left shoes on the horizontal axis.
(b) Describe indifference maps for James and Karen.
(c) Draw a contract curve based on your answer in Part (b). [Hint: It will look a little different from the one you saw in class - a person on a street will not call it a curve - because two people's preferences are different.]
(d) Use a new Edgeworth box diagram to examine what will occur in each of the shoe markets if the price of a left shoe is 1 and the price of a right shoe is 2? [Note: You need not calculate the number of shoes James and Karen wish to trade given these prices. Just indicate graphically what they want to buy and sell under these prices. In which market do you observe excess demand? What do you observe in the other market?]
(e) From what you have done in the previous part, deduce the competitive equilibrium price ratio.
6. (Partial and general equilibrium analyses) [OPTIONAL: No credit will be given.] Suppose that the supplies of Gold (G) and Silver (S) are inelastic. More specifically they are given as QG = 75 and QS = 300 , respectively. The demands for Gold and Silver are given by the following equations:
QG = 975 - PG + ½ Ps,
QS = 600 - PS + ½ PG,
where PG and PS are prices of the two goods, respectively.
(a) Are the two goods substitutes or complements?
(b) What are the equilibrium prices of Gold and Silver?
(c) Draw diagrams for the two markets describing your solution from Part (b).
(d) Suppose that a new discovery of Gold doubles the quantity supplied to 150. How will this discovery affect your answer to Parts (b) and (c)?