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Given the linear supply function for a good
Given the linear supply function for a good. When the price of the goods is 620 rupiah, there is an excess of the number of goods being offered by 80 units. However, if the price is lowered by 180 rupiah, then the number of goods offered will be 90 units. If it is known that the equation of the demand for goods function is: 3Q + P = 840
Questions
1). define the supply function
2). Calculate the price and quantity of goods when there is market equilibrium
3). If sales are taxed at 100 rupiah per unit, determine the condition of the after-tax balance and the impact of the tax on the price and quantity of goods traded.
Expert Solution
1)At 620, demand of good=(840-620)/3=73.333 corresponding supply would be since excess supply at price is 80 we have quantity supplied=73.333+80=153.333=460/3 , At 620-180=$440 we hace quantity supplied=90 so demand equation can be given as P=((620-440)/(460/3-90))*Q+C(constant) gives P=180*3Q/190+C giving 19P=54Q+C at P=440 we have Q=90 putting value 19*440=54*90+C' gives C'=3500 giving supply function as 19P=54Q+3500
2) At equilibrium equating price of demand function and supply function we get 840-3Q=(54Q+3500)/19=112.2522=~112 and P=503.24
3) At 100 tax we have supply function changing to 19(P-100)=54Q+3500 which gives new equation as 19P=54Q+5400 equating P for Equilibrium we have (54Q+5400)/19=840-3Q gives Q=95.135=~95 corresponding P=(54Q+5400)/19=554.60 Hence, Taxes has increased the equilibrium price with decrease in quantity traded
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