(3)Assume that the behavior of a typical consumer and a typical producer of comm
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(3)Assume that the behavior of a typical consumer and a typical producer of commodity X can be described by the following demand and supply curves Odx=220-4Ps + 0.751-0.25Py Qsx --20 2Px 2.5Tc- 3.5C where I-consumer income Py = price of commodity Y ; a related Tc = an index of technology for C an index of total cost of production commoditv to commodity X producing commodity X (a)Comment on the behavior of the consumer and the law of demand in this market. (b)Does the behavior of the firm conform to the law of supply in the market for commodity X? Explain (c)If the price of X is S5 and the price of Y is $10 find the income elasticity of demand for this product. Is this product a luxury? A necessity? An inferior good? (d)Explain the relationship between commodity X and commodity Y. (e)Explain how technological improvement affects supply (4)(a)Briefly define “Economics" and provide an explanation of what you think are the essential benefits to consumers and producers of gaining some knowledge of economics. (b)There is general consensus that all societies face the same fundamental economic problem. Explain the nature of this problem and the factors which underlie the observed differences in economic systems.Explanation / Answer
Qdx = 220 - 4Px +0.75I - 0.25Py
Qsx = -20 + 2Px + 2.5Tc - 3.5C
(a) The demand for good x by the consumer is governed by three factors, the price of the good itself, the income of the consumer and the price os related good y.
The demand for good x is negatively related to its price that is, as the price of x goes up, its quantity demanded falls. Also, the demand for good x is positively related to the consumer's income. As the income of the consumer increases, the demand for good x increases. The demand is negatively frelated to price of good y.
The demand function follows the law of demand, that is, as the price of the commodity x increases, its quantity demanded falls.
That is, dQdx / dPx = (-)4
(b) Yes, the behaviour of the firm conforms to the law of supply. That is, as the price of good x increases, its quantity supplied will increase. This can be seen as a positive relationship between quantity supplied and the price of x in the supply function.
dQs / dPx = (+) 2
(c) Px = $5; Py = $10
Qdx = 220 - 4Px + 0.75I - 0.25Py
Qdx = 220 - (4 x 5) + 0.75I - (0.25 x 10)
Qdx = 220 - 20 + 0.75I - 2.5
Qdx = 197.5 + 0.75I
Edi = (dQ/dI) x I / Q
dQ/dI = 0.75
Edi = 0.75 x (I / 197.5 + 0.75I)
Taking LCM and solving,
Edi = [(0.75) (197.5)] / (197.5 + 0.75I)2 > 0
The income elasticity of demand is positive. Thus, the good x is positively related to income that is, it is a luxury good.
(d) Qdx = 220 - 4Px + 0.75I - 0.25Py
It can be seen that the price of good y and the demand for good x is negatively realted that is, as the pruce of y increases, the demand for x falls. Thus, it can interpreted that both these are complementary goods. As the price of one good increases, the demand for the other good falls.
(e) Qsx = -20 + 2Px + 2.5Tc - 3.5C
dQsx / dTc = 2.5
That is, as the technology improves (increases), the supply of good x also increases. Both are positively related to one another.
(You are allowed to ask one question at a time. Kindly post the other question separately. I have solved 3. Hope it helps.)
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