(This problem requires the use of calculus.) Consider a Cobb–Douglas production function with three inputs. K is capital (the number of machines), L is labor (the number of workers), and H is human capital (the number of college degrees among the workers). The production function is: Y = K^(1/3).L^(1/3).H^(1/3)(a) Derive an expression for the marginal product of labor. How does an increase in the amount of human capital affect the marginal product of labor?(b) Derive an expression for the marginal product of human capital. How does an increase in the amount of human capital affect the marginal product of human capital?(c) What is the income share paid to labor? What is the income share paid to human capital? In the national income accounts of this economy, what share of total income do you think workers would appear to receive?

Milden company has an exclusive franchise to purchase a product from the manufacturer and distribute it on the retail level. as an aid in planning, the company has decided to start using a contribution format income statement. to have data to prepare such a statement, the company has analyzed its expenses and has developed the following cost formulas: cost cost formula cost of good sold $35 per unit sold advertising expense $210,000 per quarter sales commissions 6% of sales shipping expense ? administrative salaries $145,000 per quarter insurance expense $9,000 per quarter depreciation expense $76,000 per quarter management has concluded that shipping expense is a mixed cost, containing both variable and fixed cost elements. units sold and the related shipping expense over the last eight quarters follow: quarter units sold shipping expense year 1: first 10,000 $ 119,000 second 16,000 $ 175,000 third 18,000 $ 190,000 fourth 15,000 $ 164,000 year 2: first 11,000 $ 130,000 second 17,000 $ 185,000 third 20,000 $ 210,000 fourth 13,000 $ 147,000 milden company’s president would like a cost formula derived for shipping expense so that a budgeted contribution format income statement can be prepared for the next quarter. required: 1. using the high-low method, estimate a cost formula for shipping expe