Assume that the quantity demanded (Qd) and supplied for a product, x can be modelled by a linear equation. It is observe

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Assume That The Quantity Demanded Qd And Supplied For A Product X Can Be Modelled By A Linear Equation It Is Observe 1 (102.33 KiB) Viewed 38 times

Assume that the quantity demanded (Qd) and supplied for a product, x can be modelled by a linear equation. It is observed that when the price is $28 the number of units sold in x is 44 units; when the price decreases to $12 the number of units sold in x increases to 76. The quantity supplied (Qs) for x is 40 units when the price equal to $25, when the price decreases to $15 the firm produces 20 units. (a) Obtain the demand function for quantity x, Qd. [2 marks] (b) Obtain the supply function for quantity x, Qs. [2 marks] (c) Plot the demand and supply curves in a graph (P on vertical axis and Q on the horizontal axis). [1 mark] (d) Calculate the price elasticity of demand when P=25 and P=15 and interpret your answers. [2 marks] (e) If the price increases by 12% calculate the percentage change in the quantity demanded at P= $15. [1 mark] The elasticity is: €d = percentage change in quantity demanded percentage change in price AQ.(%) AP(%) May be rearranged as: AQ(%) = AP(%) * Ed (1) Calculate the exact percentage changes at P=$15 using the equation and compare your result to (e). Comment on these results. [2 marks] (g) Calculate and identify the equilibrium quantity and price algebraically and label it in your graph. [2 marks] (h) If the government imposes a tax of $8 per unit on sellers, find the new supply curve, new equilibrium price and quantity. [2 marks] (i) Label the new equilibrium price and quantity on the graph. [1 mark] ( ) How much tax revenue does the government collect? [1 mark] (k) What are the consumer and producer share on the government's tax revenue? [1 mark]