a) A firm's production function is given by Q=10L0¹K07 The variable Q denotes output, L is labour input and K is capital

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A A Firm S Production Function Is Given By Q 10l0 K07 The Variable Q Denotes Output L Is Labour Input And K Is Capital 1 (33.06 KiB) Viewed 22 times

A A Firm S Production Function Is Given By Q 10l0 K07 The Variable Q Denotes Output L Is Labour Input And K Is Capital 2 (54.76 KiB) Viewed 22 times

a) A firm's production function is given by Q=10L0¹K07 The variable Q denotes output, L is labour input and K is capital input. i. If the quantity of labour and capital inputs doubles, what happens to the output? (10%) ii. Explain in your own words, what information in Question (1) gives about the returns to scale for this production function? Provide your own real-world example of such a production function. (10%)
b) Another firm's production function is given by Q = KL Suppose the unit cost of labour is 1, the unit cost of capital is 2 and the firm's budget is 6. i. Use the method of Lagrange multiplier to find the maximum level of output. Provide your own arguments about why this method is advantageous compared to the substitution method. (30%) ii. (10%) iii. Find the marginal product of capital and the marginal product of labour. Interpret the values obtained in Question (ii). Provide your own argument on whether this is a labour- or capital-intensive production process. Provide a real- world example of such a process. (10%) iv. Verify the ratio of marginal product to price is the same at the optimum for both inputs. (10%) V. Provide your interpretation to Question (iv). (10%) vi. Estimate the new optimal output if the firm's budget increases to 7. If you were the Chief Executive Officer, would you consider the budget increase as worthwhile for the firm? (10%)