Posted: November 2nd, 2015

Mathematics

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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