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Econ1003 Tutorial 1

1. Write the following as a single equation:

(a)

2 3 + −1 5 5

(b)

x x x + − 5 5 5

(c)

2 x 3x x + − 5 5 5

(d)

x x 1 × × 5 5 5

(e)

x x 1 × × 5 5 5x

(f)

x x 1 (g) × + 5 5 5

x x 4 × × 5 2 3

(a) 0, (b) x/5, (c) 4x/5 (d) x2/125, (e) x/125, (f) (x2 +5)/125 (g) 2x2/15

2. An executive salary is reduced from €250,000 to €200,000. The salary is reduced by (a) 10% (b) 80% (c) 20% (d) 25%. c 3. In 2010, 5% of a population of 850,100 are unemployed. The number of unemployed persons is (a) 475,050 (b) 170,020 (c) 42,505 (d) 4250,500. c 4. The exchange rate is €1 = £0.80. £10 = (a) €80 (b) €16 (c) €12.5 (d) €15 c

5. Australia can produce 500 units of good Y if it produces 0 units of good X. Alternatively it could produce 100 units of good X if it produces 0 units of Y. It can produce any linear combination in between. Derive the production possibility curve – the PPC is the equation that shows the possible combinations of X and Y Australia can produce. Draw the PPC. How would you interpret the slope of the curve? y = 500 – 5x; the slope is the opportunity cost of y in terms of units of x forgone

6. There are two inputs into a production process labour (L) and capital (K). The wage rate per unit of L is $5 and the per-unit rental cost of capital is $8. If the firm has total costs of C, right down the equation that determines these total costs.

This is an isocost curve. It shows all the combinations of L and K at the going input cost rates that will cost the firm C. Draw a number of different isocost curves for different values of C. If the firm has hired 5 units of labour and its total costs are 73, how much capital is it using?

5L + 8K = C K = 6 units

7. The supply function for a firm is given by qs = 40 + 2P, where qs is the quantity supplied and P is the market price. The inverse demand curve is P = 100 – 1/2qd, where qd is the quantity demanded. Draw these two curve on a diagram with q on the x axis and P on the y axis. At what P and q do the curves intersect? Interpret this point. P* = 40, q* = 120 units. This is the market equilibrium P and q.

8. A consumer has income of M and can consume either good 1 at p1 or good 2 at p2. What are all the affordable bundles for the consumer? What is her budget constraint? What is the slope of the BC and what is its meaning? The government places an ad valorem tax on all goods of t percent. Determine the new BC for the consumer and explain what has happened to the BC. What is the equivalent income tax to the tax of t on all goods?

p1x1 + p2x2 ≤ M; the BC holds with equality. The slope of the BC is –p1/p2 New BC is (1+t)p1x1 + (1+t)p2x2 = M Note that the slope of the curve is unchanged – relative prices stay the same. The equivalent income tax is the tax which gives rise to the same change in real income> the change in real income is M – M/(1+t) = tM/(1+t) The equivalent income tax is then t/(1+t)...