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Green is looking to establish a new market producing energy gummy bears.
1. Green is looking to establish a new market producing energy gummy bears. After intensive research Green has found the production function is given by q = 75K1/3L2/3, where q is thousands of pounds of energy gummy bears, known as GreenergiesTM, K is capital, L is labor, r is the price of capital, w is the price of labor, and q is per year.
a. Find K and L as a function of r, w and q.
b. Use K(r, w, q) and L(r, w, q) to find the long-run cost function C(q). Discuss why someone might want to know this functional relationship.
c. What returns to scale does C(q) exhibit? How do you know and why might the long-run returns to scale make sense in this case?
d. The price of capital is given by r = $100,000, the wage is w = $25,000, and market research indicates that the market will support q = 300. What are the optimal levels of K and L?
e. What is the cost of producing q = 300 units of output?
f. Suppose Green invests in the optimal level of capital, find the short-run production function?
g. What are the functional forms of the short-run variable costs, total cost, marginal cost, average cost, and average variable cost functions?
h. What is the conceptual difference between the long-run and short-run total cost functions?
i. What are the short-run break-even quantity and price, qE and pE?
j. How much will Green produce if the price is $1,500?
k. Is the energy gummy market in long run equilibrium when p = $1,500? Show your work and explain.
l. Suppose w decreases to $22,000, what are the new qE, pE and LE?
