Let’s model the market for maple syrup of a small fictional economy. We start by making assumptions on consumer’s preferences so as to derive the market demand. Suppose 2,000 families live in the small country and that the typical family has utility from maple syrup (m) and expenditure on other products (e) equal to U(m,e) = 20m – m^2 + e. The quantity of maple syrup (m) is measured in pints per month, while expenditure on other items (e) is measured in dollars.
Assuming families allocate their budget in a rational way, find the demand for maple syrup of the typical family.
1. Aggregating across families, find the market demand for maple syrup.
2. Now, turn your attention to the supply side. Assume that 100 firms sell maple-syrup. The typical firm has a short run total cost of TC(q) = 0.1q^2 + 8q + 40 where q is measured in pints per month.
3. Assuming that each firm chooses output to maximize profit, find the supply of maple syrup of the typical firm.
4. Find the market supply of maple syrup.
5. Find the equilibrium price, the equilibrium market quantity, the number of pints of maple syrup each family buys each month, and the number of pints of maple syrup each firm sells each month.
6. In a diagram, illustrate the market demand, the market supply and the market equilibrium.
Suppose a new trade agreement allows firms to sell maple syrup abroad at a unit price of $18.
7. Illustrate this event in your demand/supply diagram adding a horizontal foreign demand curve at the price of $18.
8. How does the new trade agreement affect the domestic market for maple syrup?
9. How does the trade agreement affect buyers’ welfare and sellers’ profits?
10. How much money should government pay buyers of maple syrup to fully compensate them for the higher price of maple syrup?