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A firm produces cellphones (y) with two factors of production: labor (l) and capital (k). Its technology is represented by the production functiony=lk².

(a) Represent graphically the isoquants of levels 1, 2, and 3. Does this technology exhibit increasing, constant, or decreasing returns to scale? Why?

(b) Suppose that the prices of the inputs are 10 and 100 dollars, respectively. If the firm wants to produce one I-phone, how many units of labor and how many units of capital should it hire? How much will it cost? What if the firm wants to produce two cellphones?

(c) Derive the conditional factor demands.

(d) Derive the long run cost function of this firm if the factor prices are the ones given above. Derive the long run average cost function and the long run marginal cost function. Graph the average and the marginal cost functions.

(e) Suppose the amount of capital is fixed at 1 unit. What is the short run production function? Derive (for the given prices) the short run cost function. Derive and represent graphically the average variable cost, the average total cost, and the marginal cost functions.

(f) Derive the long-run and short-run supply curves for the firm.