Reference no: EM132422736

A firm uses two inputs, unskilled labor, L, and capital, K, to produce its product. The wage rate for one unit of labor is £5 while units of capital cost £20.

(a) Graphically depict the isocost line for a £1000 expenditure by the firm on inputs. Label the intercepts. Draw a typical isoquant (for instance one that can be derived from a Cobb-Douglas production function) for an output level, Q0, to depict the optimal input levels, L and K, for Q0 and C0 = £1000.

(b) Suppose the government institutes a minimum wage for unskilled labor of £6 per unit. In the short run, with capital fixed at K, show graphically how much it would cost the firm to hold its output constant at Q0.

(c) Show the optimal factor mix the firm will use in the long run to produce Q0, given the minimum wage.

(d) Suppose the government introduces a tax on capital of £2 per unit used. Show the optimal factor mix the firm will use in the long run to produce Q0 with the new tax on capital.

(e) Suppose the government institutes a subsidy for hiring unskilled labor of £3 per unit of labor. Graphically depict the new isocost line for a £1000 expenditure by the firm on inputs. Depict also the optimal input levels, L and K, for Q0 and C0 = £1000 with the subsidy.

AND

Alice and Bob have £100, 000 to bequeath to their two children, Carrie and Danny. Bob's preferences are represented by U(xc, xd) = xc + xd where xc is the amount of money left to Carrie, and xd is the amount of money left to Danny.

Alice's preferences are represented by U(xc, xd) = min{xc, xd} That is, Alice's utility is equal to the minimum bequest left for either of her children: for instance, if Danny received £50 and Carrie received £40, Alice would obtain a utility of 40. Whichever parent survives the longest decides how to arrange their will, and so, decides the sums bequeathed to each child.

a) In what sense do Alice and Bob face a budget constraint? In separate graphs, one each for Alice and for Bob, draw the parent's budget constraint. (Hint 1: Think of the two bequests as goods from which Alice and Bob derive utility. Hint 2: What are these goods' prices? Hint 3: Remember to label all graphs, axes, and intercepts.)

b) On each of the parent's graphs, draw 3 points representing "consumption bundles" giving different levels of utility, per the utility functions given. Include at least one point that lies on the budget constraint. Label each point with its coordinates and with the level of utility associated with it

c) To what extent do you agree with the following claim?: "Even though the parents have different preferences, both parents love their children equally." Explain.

d) Explain why Alice will always divide the bequests equally.