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प्रश्न
Complete the following activity to find MPC, MPS, APC and APS, if the expenditure Ec of a person with income I is given as:
Ec = (0.0003)I2 + (0.075)I2
when I = 1000
उत्तर
Given, EC = (0.0003)I2 + (0.075)I2
We have APC = `E_C/I`
= (0.0003). I + 0.075
At I = 1000,
APC = (0.0003) × 1000 + 0.075
= 0.3 + 0.075
∴ APC = 0.375
Now, MPC = `(d(E_C))/(dI)`
= 2 × (0.0003).1 + 0.075
= (0.0006) × I + 0.075
When I = 1000
MPC = 0.6 + 0.075
= 0.675
At I = 1000, MPS = 1 – MPC
= 1 – 0.675
= 0.325
At I = 1000,
APS = 1 – APC = 1 – 0375
= 0.625
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Fill in the blank:
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The manufacturing company produces x items at the total cost of ₹ 180 + 4x. The demand function for this product is P = (240 − 𝑥). Find x for which profit is increasing
A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price per item is given as p = 120 – x. Find the value of x for which revenue is increasing
Solution: Total cost C = 40 + 2x and Price p = 120 – x
Revenue R = `square`
Differentiating w.r.t. x,
∴ `("dR")/("d"x) = square`
Since Revenue is increasing,
∴ `("dR")/("d"x)` > 0
∴ Revenue is increasing for `square`
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Solution: Total cost C = 40 + 2x and Price p = 120 − x
Profit π = R – C
∴ π = `square`
Differentiating w.r.t. x,
`("d"pi)/("d"x)` = `square`
Since Profit is increasing,
`("d"pi)/("d"x)` > 0
∴ Profit is increasing for `square`
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p = 120 – x
∴ x = 120 – p
Differentiating w.r.t. p,
`("d"x)/("dp")` = `square`
∴ Elasticity of demand is given by η = `- "P"/x*("d"x)/("dp")`
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Then C = standing charges + labour charges + processing charges
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Differentiating w.r.t. Q, we get
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If profit is increasing , then `(dpi)/(dQ) >0`
∴ `Q < square`
Hence, profit is increasing for `Q < square`
