Final answer:
As the price is lowered from the choke price to zero for a good defined by the linear equation Q = 160 - 4P, total expenditures initially increase due to the increase in quantity demanded, but eventually will decrease as the lower price fails to compensate for the higher quantity demanded.
Step-by-step explanation:
When considering the demand for a good defined by the linear equation Q = 160 - 4P, where Q is the quantity demanded and P is the price, as the price is lowered from the choke price to zero, we observe changes in the total expenditures on the good. The choke price is the price at which quantity demanded would be zero, which is $40 in this equation. As price decreases from this point, quantity demanded increases.
If we want to understand how total expenditures, which are calculated as price multiplied by quantity (P × Q), change with price, we need to analyze the rate at which the increase in quantity offsets the decrease in price. The total expenditure initially increases as the price decreases because the increase in quantity demanded more than compensates for the lower price. However, this trend will not continue indefinitely. At some point, the extra quantity demanded does not make up for the lower price, and total expenditures will start to decrease. This relationship forms what is known as a downward-sloping curve when graphed, illustrating the initial increase followed by a eventual decrease in total expenditures as the price drops toward zero. Economists refer to this effect as the price elasticity of demand.