# Suppose the suply function of product x is given by

Suppose the suply function of product x is given by ${Q}_{x}^{S}=-30+2Px-4Pz$
a. how much of product x is produced when $Px=\mathrm{}80$ and $Pz=\mathrm{}60$
b. $Pz=\mathrm{}60$. Determine the supply function and inverse supply function for good x.
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Barbara Meeker
a) Supply function of product x is given below.
${Q}_{x}^{S}=-300+2Px-4pz$
Suppose the price of good X is $80 and price of good Y is$60, the quantity supply of good X is calculated as follows.
${Q}_{x}^{S}=-30+2Px-4Pz$
${Q}_{x}^{S}=-30+2\left(80\right)-4\left(60\right)$
${Q}_{x}^{S}=-30+160-240$
${Q}_{x}^{S}=-110$
The quantity supply of good is X is -110 units. As quantity is negative, the production of goods X will not take place.
b) Suppose the price of good Z is \$60 the supply functions= for good X is shown below.
${Q}_{x}^{S}=-30+2Px-4Pz$
${Q}_{x}^{S}=-30+2Px-4\left(60\right)$
${Q}_{x}^{S}=-30+2Px-240$
${Q}_{x}^{S}=2Px-270$
The supply function is ${Q}_{x}^{S}=2Px-270$