1. Show as we did for indifference curves, under what conditions we expect that (Hint: in your answers, you should, where appropriate, be referring to concepts such as the marginal rate of technical substitution, marginal product, transitivity, and so on): (i) Isoquants slope downwards. (ii) lsoquants further from the origin represent higher output. (iii) Isoquants cannot intersect. (iv) Isoquants are convex. 1. A firm has a production function given by the following table: Units of Labor 1 2 3 4 5 K = 3 8 12 15 17 K=2 10 15 19 22 24 K=3 16 21 25 28 30 K=4 2O 25 28 3O 31 (i) Suppose that K is fixed at 2. Does this production function exhibit diminishing marginal returns? (ii) Does this production function exhibit constant returns to scale for all values of K and L? 3. Suppose that Poland Spring has the following production function for bottled water: (3 = K+10L\"'2 (i) What is the marginal product of capital and marginal product of labor given this production function? (ii) What is the marginal rate of technical substitution of labor for capital? (iii) Initially, Poland Spring has 0 units of capital and pays $2 per unit of capital and $3 per unit of labor. What are Poland Spring's shortrun total costs as a function of the quantity it produces? What are Poland Spring's shortrun average costs and marginal costs