11. Capital market Contents nderiving the demand for capital nderiving the demand for investments nderiving the supply of savings nHayekian triangle Demand for capital nwe assume perfect competition capital market ncapital is homogenous – it is possible to use the capital for whatever type of production nin general: capital as a material or as the capital equipment (machines etc.) nwe assume: the entire capital = capital equipment nvolume of labour is fixed nfirms´ aim: maximal economic profit nfirm leases the capital equipment – it is not the owner nfirm demands such volume of capital that maximizes the economic profit... for K* stands: nMRPK = MFCK nMRPK = MR . MPK nMPK is decreasing with increasing volume of capital leased (we assume fixed volume of labour) nMFCK = r, rental, derived from the market equilibrium real interest rate Demand for capital – case of leasing Demand for capital – case of leasing r K rt capital market firm D S MFCK=AFCK= r =sK rt Kt MRPK=dK r K S' rt+1 rt+1 Kt+1 firm´s demand for capital is equal to the MRPK, which represents perfect relationship between the real interest rate and volume of leased capital nfirm invests in the capital eqpuipment – becomes the owner of the capital equipment ndifferent structure of costs on capital: R + D nR…sacrificed interest nD…sum of the capital depreciation n nR = r.P a D = δ.P nr…sacrificed interest rate nδ…rate of capital depreciation nP…capital purchase price n nthe marginal factor costs on capital: MFCK=r+δ nfor K* stands: MRPK=MFCK → MRPK=r+δ → MRPK–δ=r Demand for capital – firm is the owner Demand for capital – firm is the owner r K rt capital market firm D S MFCK=AFCK= r =sK rt Kt MRPK-δ =dK r K S' rt+1 rt+1 Kt+1 demand for capital equals to MRPK – δ MRPK =dK MRPK =dK = demand for capital in the case of leasing Deriving the demand for investments nINVESTMENTS = allocation of firm´s expenditures into the capital equipment with the aim to appreciate them nGross Investments = Net Investments + Depreciation (Restitution Investments) nRestitution Investments = necessary to keep the capital stock constant → IR=δ.K=K–(1-δ).K nNet Investments = increase of the capital stock Deriving the demand for investments r K rt firm´s demand for capital I rt Kt MRPK-δ =dK r investments rt+1 rt+1 Kt(1-δ) firm´s demand for investments Kt – desired capital stock upon rt Kt(1-δ) – capital stock after 1 period If the firm desires to keep the initial level of capital stock, it has to invest to renew the depreciated capital: Kt – Kt(1-δ), which also equals to the volume of gross investments IB IB IB IB Interest rate decreases, then the firm demands the capital stock at Kt+1. Then it has to invest to renew the depreciated capital + to invest into the new capital equipment. Gross investments increase Kt+1 r K rt firm´s demand for capital I rt Kt MRPK-δ =dK r investments rt+1 rt+1 Kt(1-δ) firm´s demand for investments IB IB Deriving the demand for investments If the interest rate increases to rt+1, firm desires to keep the capital stock after depretiation during one period – gross investments equal to zero If the interest rate increases above rt+1, firm desires to decrease the capital stock under the level after depretiation – it has to sell some capital equipment – gross investments are negative ndemand for investments more elastic than the demand for capital nupon high interest rates – possibility of firm´s negative investments non the aggregate level in a closed economy: investments cannot be negative – if a firm sells capital there must be some other firm that buys it Demand for investments - conclusions Deriving the supply of capital ncapital supply = willingness to lend disposable incomes upon different real interest rates → capital supply = supply of savings nhouseholds pick out of consumption „today“ and consumption „tomorrow“ nhouseholds would postpone present consumption to the future only upon some bonus – real interest rate nhouseholds also may consume today more than the present disposable income allows – then they become borrowers nwhat type of position (lender or borrower) is preferred depends on the households preferences – what type of position maximizes the total utility Deriving the supply of capital C0 C1 I0 I1 U(C0,C1) I0+I1/(1+r)=C0+C1/(1+r) C0=present consumption, C1=future consumption I0=present income, I1=future income I0+I1/(1+r)=C0+C1/(1+r) – budget line function: left side=present value of resources (present+future), right side=present value of consumption (present+future) budget line slope: –(1+r) if positive real interest rate, then max. value of C0< max. value of C1 slope of IC (marginal rate of time preferences) = ratio of marginal utilities of C0 and C1: –(1+τ) consumer´s equilibrium – spot of tangent of IC and BL, so if:: -(1+r) = -(1+τ), or if: r =τ in the above case the consumer does not shift present consumption to the future or vice versa The borrower C0 C1 I0 I1 U(C0,C1) I0+I1/(1+r)=C0+C1/(1+r) C0* C1* Consumer desires consume today more than the present disposable income allows – he/she must borrow. The loan equals to I0-C0* Real interest rate is positive → increase of consumption today < decrease of consumption tomorrow (consumer has to pay the interest) The lender C0 C1 I0 I1 U(C0,C1) I0+I1/(1+r)=C0+C1/(1+r) C0* C1* Consumer desires to save a part of his/her present disposable income – savings equal to: I0 – C0* Real interest rate is positiv – increase of consumption tomorrow > decrease of consumption today (consumer is paid with the interest) To derive the savings supply curve we have to analyze the impact of the change of real interest rate Increase of the real interest rate – the lender C0 C1 I0 I1 U BL C0* C1* Increase of the real interest rate induces the clock-wise rotation of BL, around the spot I0,I1 BL' SE – consumption today is substituted with consumption tomorrow–becomes relatively cheaper U' IE – induces an increase of consumption of desireable goods (consumption in whatever period is desireable) TE = SE+IE – depends on which of the partial effects prevails (here SE prevails → total effect leads to the increase of savings) Increase of the real interest rate – the borrower C0 C1 I0 I1 U BL C0* C1* BL' U' TE = SE+IE – induces a decrease of consumption in both periods – induces the increase of savings (decreases the borrower´s indebtedness) SE – consumption today is substituted with consumption tomorrow–becomes relatively cheaper IE – induces a decrease of consumption of desireable goods (consumption in whatever period is desireable) Individual supply of savings S r SS If the increase of real interest rate motivates to higher saving, then the individual supply curve of savings is positive sloped Upon low real interest rates, the individual saving might be negative But: on the aggregate level the savings cannot be negative (lender´s income effect is neutralized with borrowe´s income effect) – each lender meets a borrower On aggregate level only substitution effect matters!! Hayekian triangle na part of the Austrian theory of capital ncapital is heterogenous nexplains how additional production stages increase the economy´s product in the long run nwe use the capital market + PPF Hayekian triangle C I, production stages each production stage produces the specific volume of intermediate product – last production stage=consumption the longer horizontal leg (the more production stages) the higher level of final consumption Hayekian triangle C I, production stages S,I SS r I r* C I PPF I* I* I* Consumers wish to increase their savings – supply of savings increases, real interest rate decreases, volume of investments demanded increases SS' In the short run the economy shifts alongside the PPF towards „more investments“ and „less consumption“ – inputs shift from the late production stages to implement the new ones The horizontal leg of the triangle extends, the vertical shortens – after the new production stages are finished, the level of final consumption increases, PPF shifts rightwards – the economy grows PPF'