Archer Company is a wholesaler of custom-built air-conditioning units for commercial buildings. It gathered the following monthly data relating to units shipped and total shipping expense: Month Units Shipped Total Shipping Expense
January 3 $1,800
February 6 $2,300
March 4 $1,700
April 5 $2,000
May 7 $2,300
June 8 $2,700

Required:
Using the high-low method, estimate the cost formula for shipping expense.

Define the marginal rate of substitution between two goods (x and y). if a consumer’s preferences are given by u(x,y) = x3/4y1/4, compute the consumer’s marginal rate of substitution as a function of x and y. calculate the mrs if the consumer has chosen to consumer 48 units of x and 16 units of y. show your work. (use the back of the page if necessary.

Arnold rossiter is a 40-year-old employee of the barrington company who will retire at age 60 and expects to live to age 75. the firm has promised a retirement income of $20,000 at the end of each year following retirement until death. the firm's pension fund is expected to earn 7 percent annually on its assets and the firm uses 7% to discount pension benefits. what is barrington's annual pension contribution to the nearest dollar for mr. rossiter? (assume certainty and end-of-year cash flows.)

Suppose that fixed costs for a firm in the automobile industry (start-up costs of factories, capital equipment, and so on) are $5 billion and that variable costs are equal to $17,000 per finished automobile. because more firms increase competition in the market, the market price falls as more firms enter an automobile market, or specifically, , where n represents the number of firms in a market. assume that the initial size of the u.s. and the european automobile markets are 300 million and 533 million people, respectively.a. calculate the equilibrium number of firms in the u.s. and european automobile markets without trade.b. what is the equilibrium price of automobiles in the united states and europe if the automobile industry is closed to foreign trade? c. now suppose that the united states decides on free trade in automobiles with europe. the trade agreement with the europeans adds 533 million consumers to the automobile market, in addition to the 300 million in the united states. how many automobile firms will there be in the united states and europe combined? what will be the new equilibrium price of automobiles? d. why are prices in the united states different in (c) and (b)? are consumers better off with free trade? in what ways?