Posted: November 2nd, 2015

Mathematics

1. Simplify each of the following expressions, where possible: (a) 2? + 6? – ? +

3? (b) 5? + 2? – 5? + 4? (c) 4?

? + 3? – 43 (d) 8?

? + 4? – 6?? – 3? – 3?

? +

7?? (e) 2?

? + 5? – 2?

? – 9? (f) 3? + 6? (g) ?? – ??

2. Solve each of the following equations. Leave your answer as a fraction, if

necessary. (a) 4? + 1 = 25 (b) 4? + 5 = 5? – 7 (c) 3(3 – 2?) + 2(? – 1) = 10

(d) ?

???

= 5 (e) ?

?

=

?

???

3. Which one of the following algebraic fractions can be simplified? Explain why

the other two fractions cannot be simplified. ???

????

,

???

???

,

??

?????

.

4. The demand and supply functions of a good are given by ? = -4?? + 120

and ? =

?

?

?? + 29, respectively, where ?, ?? and ?? denote the price, quantity

demanded and quantity supplied respectively. (a) Calculate the equilibrium price and

quantity (b) Calculate the new equilibrium price and quantity after the imposition of a

fixed tax of £13 per good. Who pays the tax?

5. The demand and supply functions for two independent commodities are given

by ??? = 40 – 5?? – ?? ??? = 50 – 2?? – 4?? ??? = -3 + 4?? ??? = -7 + 3??

where ???

, ???

, ?? denote the quantity demanded, quantity supplied and price of good

? ( ? = 1,2 ) respectively. Determine the equilibrium price and quantity for this

two-quantity model. Are these goods sub stitutable or complementary?

6. The demand function of a good is ? = 100 – ? + 2? +

?

?

? ,? ,? where ?

and ? denote quantity demanded, price, income and advertising expenditure

respectively. (1) Calculate the demand where ? = 10, ? = 40 and ? = 6. Assuming

that price and income are fixed, calculate the additional advertising expenditure needed

to raise demand to 179 units. (b) Is the good inferior or superior?

7. If the consumption function is given by ? = 0.7? + 40 state the values of (a)

autonomous consumption (b) marginal propensity to consume. Transpose this formula

to express ? in terms of ? and hence find the value of ? when ? = 110.

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