Economic Analysis of a Bakery and a Farm

Tim is a baker who produces 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 + K0.5.

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

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

• Sketch Anil’s utility curve, and his budget, which is the pay he receives from his job.
• Do Anil’s 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 Anil’s individual demand, and Tim’s costs of production. 
• Determine what price and quantity would be produced if the bakery has no market power or private information. 
• What is Tim’s 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 firm’s 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 average total cost, determine his optimal consumption bundle. (He will need those doughnuts when he meets Boris later).

Boris works across town for Mac the farmer. Mac produces 50 bunches of kale per day, with Cobb-Douglas output Qkale = LK,  and faces $10 per machine hour capital rents, which are all paid by a government grant (all kale farmers who operate efficiently face zero fixed costs), and pays Boris $20 per hour for his labour. Boris then takes his pay and consumes kale and other (Marshallian) goods 

• Sketch Boris’ utility curve, and his budget constraint if kale costs $4 per bunch. Recall that Boris’ budget comes from his daily pay.
• Do Boris’ preferences satisfy the rules of preference ordering? Are there any constraints on his consumption of either good?
• Determine Boris’ optimal consumption of kale each day. 
• How many other goods can Boris purchase?

• If capital is fixed at the optimal level in the short run, determine the efficient price if Mac can act as a monopolist. Sketch the supply and demand curves, and identify the monopoly equilibrium. Donald is another farmer who faces identical costs as Mac. He is considering entering the market. 
• Determine how much profit Mac loses when Donald enters the market.
• Solve the profit for both farms once Donald has established himself in the market.

Assume Anil and Boris each arrive with a full day’s allocation of their primary good (doughnuts and kale), and nothing else. 

• Draw the Edgeworth box for Anil and Boris, and identify the initial position.
• What is the optimal quantity of doughnuts and kale for each person once they trade? Note that doughnuts and kale are infinitely divisible (i.e.: not constrained to be integers). 
• What is the new established price ratio between kale and doughnuts (Pk/Pd)?