Jake and Paul 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 = 4 K^0.75 L^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 = 3 L^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?

The sticky-price theory asserts that the output prices of some goods and services adjust slowly to changes in the price level. suppose firms announce the prices for their products in advance, based on an expected price level of 100 for the coming year. many of the firms sell their goods through catalogs and face high costs of reprinting if they change prices. the actual price level turns out to be 110. faced with high menu costs, the firms that rely on catalog sales choose not to adjust their prices. sales from catalogs will

Suppose a firm faces a fixed price of output, 푝푝= 1200. the firm hires workers from a union at a daily wage, 푤푤, to produce output according to the production function 푞푞= 2퐸퐸12. there are 225 workers in the union. any union worker who does not work for this firm is guaranteed to find nonunion employment at a wage of $96 per day. a.what is the firm’s labor demand function? b.if the firm is allowed to choose 푤푤, but then the union decides how many workers to provide (up to 225) at that wage, what wage will the firm set? how many workers will the union provide? what is the firm’s output and profit? what is the total income of the 225 union workers? c.now suppose that the union sets the wage, but the firm decides how many workers to hire at that wage (up to 225). what wage will the union set to maximize the total income of all 225 workers? how many workers will the firm hire? what is the firm’s output and profit? what is the total income of the 225 union workers? [hint: to maximize total income of union, take the first order condition with respect to w and set equal to 0.]

If a product goes up in price, and the demand for it drops, that product's demand is a. elastic b. inelastic c. stable d. fixed select the best answer from the choices provided