Compute the tax revenue collected by the government
Question 1
The demand for wine is given by the equation QD = 500 – 20P, where P is the price of wine per litre and QD is the quantity of wine demanded in litres. The supply of wine is given by the equation QS = 30P.
(a) Solve for the equilibrium quantity and price of wine. Use a wine market diagram to show this equilibrium point.
(b) Suppose that a $1 per litre tax is levied on the wine producers. Calculate the new equilibrium quantity and price of wine after tax. Use a wine market diagram to show this equilibrium point.
(c) Compute the tax revenue collected by the government. Is it correct to say that since the tax is imposed on the wine producers, the tax burden is fully shouldered by the wine producers and the wine consumers did not pay the tax at all? Explain.
(d) Determine the deadweight loss due to the tax.
Question 2
Selina has $30 to spend on ice-cream and sandwiches. Her marginal utility for ice-cream and sandwich for various quantities are shown in the table below:
| Quantity | Marginal Utility of Ice-cream | Marginal Utility of Sandwiches |
| 1 | 15 | 48 |
| 2 | 12 | 36 |
| 3 | 9 | 30 |
| 4 | 6 | 24 |
| 5 | 3 | 18 |
| 6 | 2 | 9 |
The price of ice-cream is $3 per unit and the price of sandwich is $6 per unit
(a) Since the marginal utility of sandwiches is higher than that of ice-cream for all units, it is efficient for Selina to spend all her money on sandwiches and buy 5 units of sandwiches but no ice-cream. Do you agree? Explain.
(b) Define and explain the rational spending rule. Apply this rule to identify the possible combinations of ice-cream and sandwiches that may maximise Selina’s utility.
(c) Among the combinations in (b), find the combination which Selina maximises her total utility from the two goods.
Question 3
John is working as a teacher and earning salary of $40,000 per year. He decides to quit his job and starts his own business selling computers. To buy the necessary machines and equipment, he withdraws his savings of $20,000 from his bank, where it had been earning interest of $1,000 per year. He uses a shop house inherited from his family to operate the business. Prior to his business the shop house was rented out for $100 per month. He also hires an assistant for $1,250 per month. He managed to produce 50 computers in the first year and he sold all the computers at a unit price of $1,000.
(a) Describe and calculate the annual explicit cost and implicit cost incurred by John.
(b) Describe and calculate the annual accounting profit and economic profit for John.
(c) So long as John is making a positive accounting profit from selling computers, he should remain selling computers and should not return to his previous job as a teacher. Do you agree? Explain.
Question 4
The following table shows the short run total cost incurred by a perfectly competitive firm in the short run. The firm is able to sell any amount of its output at the price of $10 per unit.
| Output | Total Cost |
| 0 | 10 |
| 1 | 16 |
| 2 | 20 |
| 3 | 22 |
| 4 | 23 |
| 5 | 26 |
| 6 | 36 |
| 7 | 48 |
| 8 | 61 |
| 9 | 81 |
| 10 | 106 |
(a) Describe the characteristics of short run. Calculate the short run average fixed cost at 4 units of output, the average variable cost at 5 units of output, the average total cost at 6 units and the marginal cost at 7th unit of output.
(b) Explain the profit maximising condition, determine the optimal quantity and calculate the total profit or loss at that quantity.
(c) Discuss the profit situation of this firm in the long run.
