a. Calculate the income elasticity of demand when Q = 20 and Y = 150 and Px = 3, Py = 1, m = 48 interpret your answer . b. Calculate the cross-price elasticity of demand when Q = 2 and Ps = 1 and interpret your answer. Section 3: Production Theory (30 Marks) Section 2: Consumer Theory (30 Marks) 1. Assume that a firm has the following production function: q = 0.5 10.4. 1. A consumer's preference map is shown: a. Calculate output when L = 100 K = 32. b. What returns to scale does this production function exhibit? C. Calculate output if technology utilized by the firm increases by 15%. d. Determine, both, the marginal product of labour and capital functions (ignore C . ) . C e. Calculate, both, the marginal product of labour and capital when L = 100, K = 32 and interpret your answers. f. Calculate the marginal rate of technical substitution when L = 100, K = 32 and interpret your answer. 2. Assume that a firm has the following production function; q = 10.5 10.5. Its capital is fixed at K = 4. It faces a rental rate of r = $80 and a wage rate of w = $20. Good X a. Calculate the firm's fixed costs. a. Assume that the consumer's preferences can be represented with the utility b. Determine the firm's variable cost function. function U = xy. What is the associated utility of bundle c? c. Determine the firm's short run cost curve. Calculate whether the consumer would prefer bundle a or bundle f? d. Determine the average, average variable, and average fixed cost functions. e. Determine the marginal cost function. State the equation for the indifference curve that passes through bundle e. . Calculate the lowest cost, and associated quantity, that the firm can produce Are there any other bundles (as labelled on the preference map) also on this this good for in the short run. indifference curve? 2 . Given the utility function U = x0.5 0.5 calculate the utility of consuming bundle z: [36,16]. Calculate the marginal rate of substitution at this bundle and interpret your answer . 3. Sam budgets $50 a week for her weekday lunch. She only considers two options: sandwiches (x) which cost $5 and salads (y) which cost $10. a. Calculate and illustrate her budget constraint. b. Now assume that the price of sandwiches increases to $6.25. Calculate and add this to your illustration. c. Sam considers one sandwich and one salad to be perfect substitutes for each other. Calculate the marginal rate of substitution and the slope of the new budget constraint (from b.). d. Determine her optimal bundle and add this to your illustration appropriately. 4. Use the following information to calculate Ben's optimal bundle and his resulting utility: IC : U ( x , y ) = x0.5 0.5