Tim is a baker who produces gourmet doughnuts. He can access labour at a rate of $2 per hour, and capital at a rate of $0.25 per machine hour. He produces doughnuts according to Q = L + K^0.5.

If the bakery is operating with an optimal factor allocation, and producing 40 doughnuts per week, determine the average total cost of a doughnut.

The bakery employs one labourer, Anil, who consumes doughnuts (d) and other goods (y) with utility U(d,y) = e^d y. (Assume y is the Marshallian good, with P_Y=$1).

Sketch Anils utility curve, and his budget, which is the pay he receives from his job each week.

Do Anils preferences satisfy the rules of preference ordering? Are there any constraints on his consumption of either good?

Derive the supply and demand curves based on Anils individual demand, and Tims costs of production.

Determine what price and quantity would be produced if the bakery has no market power or private information.

What is Tims profit if he can sell the perfectly competitive number of goods?

What price and quantity will Tim choose if he can exert monopoly power?

What is the firms per-unit profit if Tim sells the monopoly number of goods?

What would be the loss in consumer surplus between the two prices?

How much producer surplus is gained when Tim acts as a monopolist?

What is the size of the resulting dead-weight loss?

Sketch the supply and demand curves, and identify on the graph the equilibrium prices and quantities, along with the surpluses and DWL.

If Anil can purchase doughnuts at their marginal cost, determine his optimal consumption bundle. (He will need those doughnuts when he meets Boris later).