Aerodynamics is a company specializing in the production of bicycle shirts. It has a fixed capital stock, and sells its shirts for $20 each. It pays a weekly wage of $400 per worker. Aerodynamics must maximize its profits by determining the optimal number of employees to hire. The marginal product of each worker can be inferred from the table below. Determine the optimal number of employees. [Hint: You must determine the VMPL schedule, having first computed the MPL.]
Employment |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
Total output |
0 |
20 |
50 |
75 |
95 |
110 |
120 |
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Suppose that, in Exercise 12.1 above, wages are not fixed. Instead the firm must pay $50 more to employ each individual worker: The first worker is willing to work for $250, the second for $300, the third for $350, etc. But once employed, each worker actually earns the same wage. Determine the optimal number of workers to be employed. [Hint: You must recognize that each worker earns the same wage; so when one additional worker is hired, the wage must increase to all workers employed.]
Consider the following supply and demand equations for berry pickers. Demand: W=22–0.4L; supply: W=10+0.2L.
- For values of , calculate the corresponding wage in each of the supply and demand functions.
- Using the data from part (a), plot and identify the equilibrium wage and quantity of labour.
- Illustrate in the diagram the areas defining transfer earnings and rent.
- Compute the transfer earnings and rent components of the total wage bill.
The rows of the following table describe the income stream for three different capital investments. The income flows accrue in years 1 and 2. Only year 2 returns need to be discounted. The rate of interest is the first entry in each row, and the project cost is the final entry.
Interest rate |
Year 1 |
Year 2 |
Cost |
8% |
8,000 |
9,000 |
16,000 |
6% |
0 |
1,000 |
900 |
10% |
4,000 |
5,000 |
11,000 |
- For each investment calculate the present value of the stream of services.
- Decide whether or not the investment should be undertaken.
Nihilist Nicotine is a small tobacco farm in south-western Ontario. It has three plots of land, each with a different productivity, in that the annual yield differs across plots. The output from each plot is given in the table below. Each plot is the same size and requires 3 workers and one machine to harvest the leaves. The cost of these inputs is $10,000. If the price of each kilogram of leaves is $4, how many plots should be planted?
Land plot |
Leaf yield in kilograms |
One |
3,000 |
Two |
2,500 |
Three |
2,000 |
The timing of wine sales is a frequent problem encountered by vintners. This is because many red wines improve with age. Let us suppose you own a particular vintage and you envisage that each bottle should increase in value by 10% the first year, 9% the second year, 8% the third year, etc.
- Suppose the interest rate is 5%, for how many years would you hold the wine if there is no storage cost?
- If in addition to interest rate costs, there is a cost of storing the wine that equals 2% of the wine's value each year, for how many years would you hold the wine before selling?
Optional: The industry demand for plumbers is given by the equation W=50–0.08L, and there is a fixed supply of 300 qualified plumbers.
- Draw a diagram illustrating the supply, demand and equilibrium, knowing that the quantity intercept for the demand equation is 625.
- Solve the supply and demand equations for the equilibrium wage, W.
- If the plumbers now form a union, and supply their labour at a wage of $30 per hour, illustrate the new equilibrium on your diagram and calculate the new level of employment.