1. Jane, the manager of a company manufacturing air-conditioning units can choose between two production technologies for a new product line. If she chooses and installs technology 1, the yearly costs will be C1(q) = 3600 + 65q + 36q2. If she installs technology 2, they will be C2(q) = 900 + 900q + q2.
a. What are the average total costs of production for each technology? What are the average variable costs of production?
b. Which technology would Jane prefer (purely from a cost standpoint) if the company expected to sell 30 units in summer and 10 units in winter each year?
c. The marginal cost associated with these two technologies are MC1 = 65 + 72q and MC2 = 900 + 2q respectively. At what level of output, the average cost will be minimized for both technologies?
2.a. The supply curve for butter is: Qs = 500 + 2P, where Qs is the quantity supplied of butter( in millions of pound per year) and P is the price of butter per year. The demand curve for butter is a vertical line at Qd = 504 millions of pounds per year. What is the equilibrium price of butter?
b. If the government imposes a controlled price of $1 per pound on butter, will there be an excess supply or excess demand of butter? How big will it be?
c. The federal government recently decided to raise the excise tax on hard liquor. Graphically illustrate the effects of this tax on the market for hard liquor
i.e., how will it effect demand and/or supply and price? Explain with a diagram. How would this tax affect a beer distributor? Explain with a diagram.
3. The demand for company X's product is given by: Qx= 16 - 2Px - 3Py + I, where Qx is quantity of good X, Px is price of good X, Py is price of good Y and I is income.
a. What will be the demand curve for good X if income is $100 and price of Y is $4?
b. What is the price elasticity of good X when price of good X is $7? Is the demand elastic or inelastic? If the company wants to increase its revenue, should it increase or decrease its price and why?
c. A manufacturer has paid an engineering firm $300,000 to design a new plant, and it will cost another $2 million to build the plant. In the meantime, however, the manufacturer has learned of a foreign company that offers to build an equivalent plant for $2,200,000. What should the manufacturer do and why?
4. A business has the following demand and cost structure.
Demand: P = 15 - Q; marginal revenue => MR = 15-2Q
Total Cost: C = 5 + 3Q; marginal cost MC = 3.
a. What is the profit maximizing price, output, and total profit?
b. What would be the revenue maximizing price, output and revenue?
c. In your opinion, which one of these two above solutions is better? Why?