If the retail price of a particular item produced by a firm is £P then the number of itemsthe firm is prepared to supply at this price is given by the equation1 92S P= −whilst the number D of items that customers will buy at this price is given by theequation136 3D P= −(a) Using the same axes draw graphs of D and S against P. Indicate the pointcorresponding to the situation when the supply S equals the demand D (that is,the market is in equilibrium) and determine the number of articles produced inthis case. Find also the selling price corresponding to the equilibrium state of themarket.(b) When the government levies a tax of £10 per item sold, the customers areconcerned only with the new total retail price £P, whereas the suppliers react asthough the price was £(P – 10).
Question
If the retail price of a particular item produced by a firm is £P then the number of itemsthe firm is prepared to supply at this price is given by the equation1 92S P= −whilst the number D of items that customers will buy at this price is given by theequation136 3D P= −(a) Using the same axes draw graphs of D and S against P. Indicate the pointcorresponding to the situation when the supply S equals the demand D (that is,the market is in equilibrium) and determine the number of articles produced inthis case. Find also the selling price corresponding to the equilibrium state of themarket.(b) When the government levies a tax of £10 per item sold, the customers areconcerned only with the new total retail price £P, whereas the suppliers react asthough the price was £(P – 10).
Solution
This is a multi-step problem that involves understanding supply and demand, graphing, and solving equations. Here's how you can solve it:
(a) First, we need to find the equilibrium point, which is where the supply equals the demand. This means we need to set the two equations equal to each other and solve for P:
192 - P = 136 - 3P
Solving this equation gives P = 28.
Substituting P = 28 into either the supply or demand equation will give the number of items. Let's use the supply equation:
S = 192 - 28 = 164
So, the number of items produced at equilibrium is 164 and the selling price at equilibrium is £28.
(b) When the government levies a tax of £10 per item sold, the suppliers react as though the price was £(P – 10). This changes the supply equation to:
S = 192 - (P - 10)
Setting this equal to the demand equation and solving for P gives:
192 - (P - 10) = 136 - 3P
Solving this equation gives P = 38.
So, when a tax of £10 is levied, the new selling price is £38.
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