The Own Price Elasticity of Demand - Assignment Example

Economics Problem and 2 Question (a) The own price elasti of demand gauges the percentage change in quantity of goods demanded effected by a percentage in price and due to the law of demand the coefficient of price elasticity is negative in nature. If demand function for product Y is given by: Y = PY-1.9PZ-1.4m1.2 and in order to differentiate such an equation this formula is used. Let u be demand which is equal to Y therefore own price elasticity of product Y is eY=δu/δpy x δdy/δu, where δu/δpy = -1.9p-2.9 but u=Y= PY-1.9PZ-1.4m1.2 therefore eY=, -1.9p-2.9(PY-1.9PZ-1.4m1.2). The cross price elasticity measured the degree of responsiveness of demand of a give commodity due to the change of price in substitute or complementary goods. In this case, ey,z = → where (δu/δpz) x δy/δu but u=Y, →. ey,z = [PZ-1.4/( PY-1.9PZ-1.4m1.2)] x [-1.4PZ-2.4( PY-1.9PZ-1.4m1.2)] → PZ-1.4 x -1.4Pz-2.4 therefore ey,z = -1.4Pz-3.8. On the other side income elasticity of demand is normally used to elucidate how the buyers’ income swings the demand factor for commodities; the equation will be differentiated in respect m therefore em= but u = Y → em = 1.2m1.4 (PY-1.9PZ-1.4) Question (b) The product Y and Z are complementary goods; actually, positive cross price elasticity designates that two commodities are substitutes since the price of one commodity and demand of the other commodity positively vary. In the proviso that whenever the price of good “Y” upsurges, quantity of good “Z” also increases. On the other side a negative price elasticity of demand happens for complementary goods which do happen in the reverse direction. In this case inverse relationship between price and quantity demanded exist in the equation identified ey,z = -1.4Pz-3.8. Question (c) Form a typical look on the demand function; Y = PY-1.9PZ-1.4m1.2 of product Y, it is clearly identified as a non- linear demand or curvilinear which changes all along the curve. It yields a demand curve instead of a demand line. Generally, it takes a form of power functions which graphically a rectangular hyperbola in shape. The powers of the price variable in a non-linear function indicate the coefficient of price elasticity of demand, which is normally constant. And the equation shows that consumers expenditure “Y” will increase with the price py-1.9 if its demand is relatively inelastic. Question (d) This indicates that the income elasticity of product “Y”’s demand is positive. This consequently, shows an increase in consumer’s income leads s /he to purchase more of good “Y”. In this respect good “Y” is said to be a normal good as justified in the equation-em = 1.2m1.4 (PY-1.9PZ-1.4). Question (e) If the price of product Z is lowered by 10 percent, demand on the good Y must go up by more than 10 %( or greater than this percentage), since the quantity demanded must fall when the price goes up. Question (f) The knowledge of income elasticity would enable the control of production in these products by predicting the changes in personal income in light of economic trend. It also helps in cost saving (Musgrave, pg. 123). Question (g) Economic inflation is normally uncertain and random in occurrence aspect associated with the modern economy. The existence of this tends to lower the value of money in circulation thus causing the price of goods to sky rocket. Problem 2 Question (a) The demand function for product y is given by: Q = 50 -0.20PQ + 0.8m, The own price elasticity of demand gauges the percentage change in quantity of goods demanded effected by a percentage in price and due to the law of demand the coefficient of price elasticity is negative in nature; eQ=δdQ/δpQ. Question (b) This question calls for the determination of factor of a given product in regards to its demand. Once the price is derived output moves to consumers and the payment is realized in form the company’s revenue. This can be improved through sales promotion and value addition to the product. In most cases the objective of firms is to maximize revenue rather than profits. This is because the sale is considered as an index of performance of the firm and the financial institution will be only willing to extend their loan to a firm of growing sales (Musgrave, pg. 123). Question (c) In the economic sense, normal good are demanded in an increasing quantity as the income of the consumers’ rises. For instance, clothing will fall in this category of commodities. This therefore means that during initial stages the increase is more rapid in response to increase in income and later at a lower rate. Rationally, this is in coherence with law of demand. In the income elasticity of demand expression, a positive derivative em= δQ/δm is positive. This indicates that the income elasticity of product “Y”’s demand is positive. This consequently, shows an increase in consumer’s income leads s /he to purchase more of good “Y”. In this regard good “Y” is said to be a normal good. Problem 3 Multiple regression model development, it incorporates several independent variables in ratio to dependent variable. SUMMARY OUTPUT Regression Statistics Multiple R 0.924588 R Square 0.854862 Adjusted R Square 0.838736 Standard Error 151.1885 Observations 21 ANOVA   df SS MS F Significance F Regression 2 2423404 1211702 53.01007 2.86E-08 Residual 18 411443.2 22857.96 Total 20 2834847         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 1250.386 269.1979 4.644856 0.000201 684.8218 1815.95 684.8218 1815.95 AVERAGE INCOME 0.009125 0.003088 2.955265 0.008469 0.002638 0.015612 0.002638 0.015612 PRICE/MONTH -70.7652 16.52546 -4.28219 0.000448 -105.484 -36.0465 -105.484 -36.0465 Regression analysis is used to produce the equation to predict a dependent variable by one or more independent variables as here Y = α + β X1 + γ X2 + ε. Where, “γ” and “β” are multipliers or coefficient which describes the change of independent variable on dependent factor “Y”. In the output regression coefficients of the data above predicts subscribers =1250.386+0.009125-70.7652 with a meaning that subscriptions predicted to rise to1250.386when the average income variable rises up by 0.009125. The stat test statistics, Standard Error, 95% Confidence Interval, and P>|t| the p values also applies. As can be seen that the standard error is very insignificant indicating less variant and the absolute assessment of the t stat is relatively large. Statistically when-value is less than 0.05, it is significant at 95% level, and if it is a smaller amount than 0.01, it is significant at 99% level. α is an intercept of the regression line which is constant. Entire number of observations in data analysis is 21, F-test stat. with 2numerators, R squared was 0.854862, and elaborating 85% of the variance in “Y” is explained by the model. However, the standard deviation of 151.1885 is not expounded by the model. Work Cited Musgrave, Frank, Frank Musgrave, and EliaKacapyr.Barrons Ap Microeconomics/macroeconomics. Hauppauge, N.Y: Barrons Educational Series, 2009. Print. Read More