Miguel and jake run a paper company. each week they need to produce 1,000 reams of paper to ship to their customers. the paper plant's long-run production function is q = 4k^0.75l^0.25 , where q is the number of reams produced, k is the quantity of capital rented, and l is the quantity of labor hired. for this production function, the mpl = k^0.75 / l^0.75 and the mpk = 3l^0.25 / k^0.25 . the weekly cost function for the paper plant is c = 10k + 2l, where c is the total weekly cost

a. what ratio of capital to labor minimizes jake and paul's total costs?

b. how much capital and labor will jake and paul need to rent and hire in order to produce 1,000 reams of paper each week?

c. how much will hiring these inputs cost them?

3. saving two consumers, larry and jeff, have utility functions defined over the two periods of their lives: middle age (period zero) and retirement (period 1). they have the same income in period 0 of m dollars and they will not earn income in period 1. the interest rate they face is r. larry’s and jeff’s utility functions are as follow. = 0.5 + 0.5 and = 0.5 + 0.5 for each person is between zero and one and represents each consumer’s temporal discount econ 340: intermediate microeconomics. ben van kammen: purdue university. rate. a. write the budget constraint that applies to both jeff and larry in terms of consumption in each period and ), interest rate, and m. b. what is larry’s and what is jeff’s marginal rate of intertemporal substitution? c. what is the slope of the budget constraint? d. write each consumer’s condition for lifetime utility maximization. e. re-arrange the conditions from part (d) to solve for the ratio, . f. if > which consumer will save more of his middle age income? g. if > 1 1+ , in which period will larry consume more: = 0 or = 1?