a) The elasticity of demand is calculated using the formula: E = (dq/dp)*(p/q). In this case, the derivative of the demand function D(p) = 319 - p with respect to p is -1. So, E = (-1)*(p/(319-p)).

b) To find the elasticity at p=118, we substitute p=118 into the elasticity formula: E = (-1)*(118/(319-118)) = -0.59. Since the absolute value of this elasticity is less than 1, the demand is elastic at p=118.

c) Total revenue (TR) is calculated as the product of price and quantity, i.e., TR = p*q = p*(319-p). To find the value of p that maximizes total revenue, we take the derivative of TR with respect to p, set it equal to zero, and solve for p. The derivative of TR is 319 - 2p. Setting this equal to zero gives p = 319/2 = 159.5. So, total revenue is maximized when the price is $159.5.

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a) The elasticity of demand is calculated using the formula: E = (dq/dp)*(p/q). In this case, the derivative of the demand function D(p) = 319 - p with respect to p is -1. So, E = (-1)*(p/(319-p)).

b) To find the elasticity at p=118, we substitute p=118 into the elasticity formula: E = (-1)*(118/(319-118)) = -0.59. Since the absolute value of this elasticity is less than 1, the demand is elastic at p=118.

c) Total revenue (TR) is calculated as the product of price and quantity, i.e., TR = p*q = p*(319-p). To find the value of p that maximizes total revenue, we take the derivative of TR with respect to p, set it equal to zero, and solve for p. The derivative of TR is 319 - 2p. Setting this equal to zero gives p = 319/2 = 159.5. So, total revenue is maximized when the price is $159.5.

Knowee AI · Accepted Answer

a) The elasticity of demand is calculated using the formula: E = (dq/dp)*(p/q). In this case, the derivative of the demand function D(p) = 319 - p with respect to p is -1. So, E = (-1)*(p/(319-p)).

b) To find the elasticity at p=118, we substitute p=118 into the elasticity formula: E = (-1)*(118/(319-118)) = -0.59. Since the absolute value of this elasticity is less than 1, the demand is elastic at p=118.

c) Total revenue (TR) is calculated as the product of price and quantity, i.e., TR = p*q = p*(319-p). To find the value of p that maximizes total revenue, we take the derivative of TR with respect to p, set it equal to zero, and solve for p. The derivative of TR is 319 - 2p. Setting this equal to zero gives p = 319/2 = 159.5. So, total revenue is maximized when the price is $159.5.

for the demand function q=D(p)=319-p, find the following a) the elasticityb) the elasticity at p=118, stating whether the demand is elastic or inelastic or has unit elasticityc) the value(s) of p which total revenue is a maximum (assume that p is in dollars

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