Question

Question 1 5 pts What is the name of the slope of the isoquant? No abbreviations. 12pt Paragraph BI V A L T Owords </> Question 2 5 pts Write down the equation that decomposes the effect of a change in price on demand of a good. No abbreviations. 12pt Paragraph BI V Ave Tv

Answer 1

Question 1

Marginal rate of technical substitution (MRTS) is the amount by which a producer reduces quantity of one input (here input y) when one more unit of other input (here input x) while keeping output constant

$Q=f(x,y)\\ This\ is\ production\ function\\ MRTS=-\frac{dy}{dx}=\frac{MP_{x}}{MP_{y}}=\frac{\frac{\partial Q}{\partial x}}{\frac{\partial Q}{\partial y}}\\ MP_{x}=marginal\ product\ of\ input\ x\\ MP_{y}=marginal\ product\ of\ input\ y\\$

Question  2

Slustky equation

$price\ effect=substitution\ effect-income\ effect\\ At\ initial\ utility\ maximization\ point\, where\ utility\ is\ at\ given\ level\ \overline U,the\ following\ conditions\ hold\\ Compensated\ demand\ for\ good\ x=Marshallian\ demand\ for\ good\ x\\ x_{c}(p_{x},p_{y},\overline{U})=x(p_{x},p_{y},m)\\ p_{x}=price\ of\ good\ x\\ p_{y}=price\ of\ good\ y\\ m=income\ of\ consumer\\$

income,m equals minimum expenditure, E to achieve utility, U. Substitute expenditure function, e(pr, Py, U) in marshallian demand function Ic(pr, Py, U) = 2(Pr, Py, elpr. Py, U)) Taking partial derivative of RHS & LHS with respect to pr дходу ду де Opzopz + de * opz

$Expenditure (income),e=p_{x}x+p_{y}y\\ \frac{\partial e}{\partial p_{x}}=x$

$\frac{\partial x_{c}}{\partial p_{x}}=\frac{\partial x}{\partial p_{x}}+\frac{\partial x}{\partial e}*\frac{\partial e}{\partial p_{x}}\\ \frac{\partial x}{\partial p_{x}}=\frac{\partial x_{c}}{\partial p_{x}}-\frac{\partial x}{\partial e}*\frac{\partial e}{\partial p_{x}}\\ \frac{\partial x}{\partial p_{x}}=\frac{\partial x_{c}}{\partial p_{x}}-\frac{\partial x}{\partial e}*x\\$

changes in income and expenditure is same in case of marshallian demand function

$\frac{\partial x}{\partial p_{x}}=\frac{\partial x_{c}}{\partial p_{x}}-\frac{\partial x}{\partial e}*x\\ \frac{\partial x}{\partial p_{x}}=\frac{\partial x_{c}}{\partial p_{x}}-x\frac{\partial x}{\partial m}\\ this\ is\ slustky\ equation\\ price\ effect=substitution\ effect-income\ effect\\$

$\frac{\partial x}{\partial p_{x}}=price\ effect\\ \frac{\partial x_{c}}{\partial p_{x}}=substitution\ effect\\ x\frac{\partial x}{\partial m}=income\ effect\\$