1. Profit-Maximization in Long Run (15 points)

An electronics plant's production function isQ=L²K, whereQis its output rate,Lis the amount of labour it uses per period, andKis the amount of capital it uses per period.

1. (3 points)Calculate the marginal product of labour (MP_L) and the marginal product of capital (MP_K) for this production function.

Hint: MP_K=dQ/dK. When taking the derivative with respect toK, treat

Las constant. For example whenQ=L³K², we have:MP_K= 2L³K.

1. (3 points)Is this plant subject to decreasing or increasing returns to scale? If the use of both inputs is increased by 100%, will the output rise by less or more than 100%? Please explain and show mathematically.
2. The firm's vice president for manufacturing hires you to determine which com- bination of inputs the plant should use to produce 1,000 units of output. The price of labor is $4 per unit, and the price of capital is $2 per unit. What advice would you give her?
3. (5 points)In what ratio should inputs be used to maximize profits?
4. (4 points)How many units of labour and capital should be employed to produce 1,000 units of output?