In: Economics
Imagine you have a farm with three plots of land. There is one in the valley, one on the hill and one in the swamp. Each plot can either grow corn or wheat. Assume that planting, harvesting, etc. is free. The quantity of each crop on each plot is given by the following table.
Plot Corn Wheat
Valley 200 300
Hill 150 450
Swamp 100 100
a. Draw a PPF for your farm. Indicate all slopes and intercepts.
b. If the price of corn is $5/unit and the price of wheat is $2/unit, what should you produce on each plot in order to maximize revenue? (We haven't said the word "revenue" yet but it means the total market value of the crops.)
c. If the price of corn is $2.50 and the price of wheat is $2, what do you want to produce on each plot?
a. production possibility frontier is the different combinations in which the two crops can be produced. For instance, Corn in Plot and Valley and Wheat in Swamp, and so on. Let's tabulate them and then plot the PPF.
Corn in | Wheat in | Qty of Corn | Qty of Wheat |
All 3 | None | 450 | 0 |
Valley, Hill | Swamp | 350 | 100 |
Valley | Hill, Swamp | 200 | 550 |
Hill | Valley, Swamp | 150 | 400 |
Swamp | Valley, Hill | 100 | 750 |
None | All 3 | 0 | 850 |
b. Pls see table below
Qty * Price | Qty * Price | |||||||
Plot | Quantity of Corn | Quantity of Wheat | Price of Corn | Price of Wheat | Revenue from Corn | Revenue from Wheat | Higher of the two | We will produce |
Valley | 200 | 300 | 5 | 2 | 1000 | 600 | 1000 | Corn |
Hill | 150 | 450 | 5 | 2 | 750 | 900 | 900 | Wheat |
Swamp | 100 | 100 | 5 | 2 | 500 | 200 | 500 | Corn |
c. Pls see table below
Qty * Price | Qty * Price | |||||||
Plot | Quantity of Corn | Quantity of Wheat | Price of Corn | Price of Wheat | Revenue from Corn | Revenue from Wheat | Higher of the two | We will produce |
Valley | 200 | 300 | 2.5 | 2 | 500 | 600 | 600 | Wheat |
Hill | 150 | 450 | 2.5 | 2 | 375 | 900 | 900 | Wheat |
Swamp | 100 | 100 | 2.5 | 2 | 250 | 200 | 250 | Corn |