Hi, I'm after some assistance with some microeconomics questions, any help is much appreciated.

1. True, false, or uncertain: The difference between price and a firm's marginal cost is the amount of profit for the firm per unit of output, and the firm makes its choice(s) so that this difference (between price and marginal cost) is as large as possible. Explain your answer. 2. A firm's production function is given by q = vZ + K . The price of labour is fixed at w = 1, and the price of capital is fixed at r = 8. a. Find the firm's marginal rate of technical substitution. b. Suppose both labour and capital can be varied by the firm, and that the firm wishes to produce q units of output. Use the answer to (a) to find the cost-minimising amounts of labour and capital (as functions of q). You may assume, here and for the other parts of this question, that q 24. c. Use the answer to (b) to find the firm's cost function, and from this, its marginal and average cost functions. d. For which values of q does this firm face economies of scale? Diseconomies of scale? e. Explain in words the way this firm expands production as output rises. 3. John's Lawn Mowing Service is a small business that acts as a price taker. The market price of lawn mowing is $20 per lawn. John's costs (in dollars) are given by c(q) = 0.1q~ + 10q + 50, where q is the number of lawns John mows in a week. a. How many lawns should John mow each week in order to maximize profit? b. Calculate John's maximum weekly profit. C. What is John's supply curve