1. Chloe consumes chicken wing (x) and beer (y). Let Px+Py=M be Chloe's budget constraint and her utility function is U(x, y)=5xy.
a. Find the formula of income-consumption curve. (This is nothing new. You have solved this many times before.)
b. Find the demand functions of chicken wing.
c. Draw Chloe's Engel curve for chicken wing from question (c) above.
d. What are the price elasticities of demand for chicken wing? What are the income elasticities of demand for beer?
2. Suppose that the production function of a representative firm in perfect competition is given as X=K^0.25L^0.75 and the budget of this firm is defined as PL+PK=C for arbitrary C.
a. Derive the Long-run expansion path.
b. Suppose that PL (wage) is 1 and PK (rent for capital) is 2. Current the available budget limit is 12 and plant size (fixed level of capital) is Ko=3. Find the demand for labor. Is this cost minimizing level of labor employment?
c. Now suppose that the plant size (level of capital) can be adjustable under same input price & budget condition in question 4-(b). Find the demand for labor.
d. Now drop previous assumption about price of labor, price of capital and budget limit, and just focus on the general case. Find the formula of total cost function, marginal cost function, and average cost function in the long-run. (Hint: TC(X)= PL×L + PK×K. Plug input demand functions into L and K of TC function. Input demand functions are derived by plugging rearranged production function with respect to L or K into the formula of expansion path.)